{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DHFDAHTYX7DAZAXBS4VNIJGI6Y","short_pith_number":"pith:DHFDAHTY","schema_version":"1.0","canonical_sha256":"19ca301e78bfc60c82e1972ad424c8f61b6f44adb309d1a76da76c50981412d2","source":{"kind":"arxiv","id":"1304.6420","version":1},"attestation_state":"computed","paper":{"title":"Preventing Unraveling in Social Networks Gets Harder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.SI","authors_text":"Fedor V. Fomin, Petr A. Golovach, Rajesh Chitnis","submitted_at":"2013-04-23T20:44:07Z","abstract_excerpt":"The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \\cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each individual derives a benefit proportional to the number of its friends which are engaged. Given a threshold degree $k$ the equilibrium for this model is a maximal subgraph whose minimum degree is $\\geq k$. However the dropping out of individuals with degrees less than $k$ might lead to a cascading effect of iterated withdrawals such that the size of equilibrium "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.6420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2013-04-23T20:44:07Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"9853289d0e895a9d291fa5b6c62307428007ca1aac0fac17c8b438639e7e6fbc","abstract_canon_sha256":"034d8f003401cf7dac9ce24147439e7777566deb41738c5efbf8099774e39062"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:13.170114Z","signature_b64":"b4QU5oB/8nLNzDiBErbSjIzMTBp/GQiBt+9PbJq8g4S1qkkmD5srm9ABvQUFVc6nMj5p1h80hbaiayVNZ4zcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19ca301e78bfc60c82e1972ad424c8f61b6f44adb309d1a76da76c50981412d2","last_reissued_at":"2026-05-18T03:27:13.169501Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:13.169501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Preventing Unraveling in Social Networks Gets Harder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.SI","authors_text":"Fedor V. Fomin, Petr A. Golovach, Rajesh Chitnis","submitted_at":"2013-04-23T20:44:07Z","abstract_excerpt":"The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \\cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each individual derives a benefit proportional to the number of its friends which are engaged. Given a threshold degree $k$ the equilibrium for this model is a maximal subgraph whose minimum degree is $\\geq k$. However the dropping out of individuals with degrees less than $k$ might lead to a cascading effect of iterated withdrawals such that the size of equilibrium "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6420","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.6420","created_at":"2026-05-18T03:27:13.169591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.6420v1","created_at":"2026-05-18T03:27:13.169591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6420","created_at":"2026-05-18T03:27:13.169591+00:00"},{"alias_kind":"pith_short_12","alias_value":"DHFDAHTYX7DA","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DHFDAHTYX7DAZAXB","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DHFDAHTY","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y","json":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y.json","graph_json":"https://pith.science/api/pith-number/DHFDAHTYX7DAZAXBS4VNIJGI6Y/graph.json","events_json":"https://pith.science/api/pith-number/DHFDAHTYX7DAZAXBS4VNIJGI6Y/events.json","paper":"https://pith.science/paper/DHFDAHTY"},"agent_actions":{"view_html":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y","download_json":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y.json","view_paper":"https://pith.science/paper/DHFDAHTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.6420&json=true","fetch_graph":"https://pith.science/api/pith-number/DHFDAHTYX7DAZAXBS4VNIJGI6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/DHFDAHTYX7DAZAXBS4VNIJGI6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y/action/storage_attestation","attest_author":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y/action/author_attestation","sign_citation":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y/action/citation_signature","submit_replication":"https://pith.science/pith/DHFDAHTYX7DAZAXBS4VNIJGI6Y/action/replication_record"}},"created_at":"2026-05-18T03:27:13.169591+00:00","updated_at":"2026-05-18T03:27:13.169591+00:00"}